Dither matrix design using sub-pixel addressability

ABSTRACT

A method of generating a dither matrix for an output device having sub-pixel addressability that permits the attenuation of tone for less than whole pixels. An original representative pixel grid is expanded to a super-resolution by replication of the pixel grid in both directions by the sub-pixel factor S. Halftoning methods for generating dither patterns are then applied using the super-resolution grid to create dither or filter outputs, which are converted to a corresponding output for a sub-pixel resolution grid. Selection of location for incremental addition (deletion) of tone is made using the sub-pixel grid output. The cycle of output generation, conversion to sub-pixel resolution, and tone modulation selection is repeated iteratively until a desired gray level is reached. The process is further repeated for each desired gray level to produce the multiple dither patterns that comprise the desired dither matrix.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to halftone images, and moreparticularly to methods of generating dither arrays for use with outputdevices having sub-pixel addressability. The techniques may beimplemented in an apparatus, as methods, or as programs of instructionsfor directing an apparatus or machine to carry out the processing stepsof these techniques.

2. Description of the Related Art

Many image rendering technologies, referred to generally herein asoutput devices, have only binary outputs with respect to any oneparticular element or pixel, whereby each pixel of the image either hasa dot printed or not printed. Input or source images, however, may havea gray scale of much greater depth, most typically 256 different tones(0 through 255) defined by 8 bits associated with each pixel. Thus, foran output device to render a gray scale image, it is necessary thereforeto convert source images comprised of higher order gray levels intohalftone images.

(A pixel is just one location on the addressable grid, whereas a dotgenerally refers to a physical positive rendering or inking which can becomposed of any number of contiguous pixels, meaning one, two or morecontiguous (or closely proximate) pixels form a single dot. In order toavoid confusion and assist the reader in more fully appreciating thepresent invention, in the present description “pixel” or “sub-pixel” andsimilar terms such as “grid” will be used to refer to the addressablelocations; whereas “pixel-dot” will refer to a single printed or turnedon pixel and “dot” will be used in referring to printed clusters of morethan one pixel.)

The problem of representing gray scale images on a binary output deviceis known as “dithering” or “halftoning.” Halftoning creates the illusionof continuous tone images by judicious arrangement of binary pictureelements, simulating the continuous tone image. Dithering relies on thefact that the human visual system integrates information over spatialregions, so that a pattern of light and dark evoke a sensationapproximating that of a uniform gray area even when the individualdisplay element can be resolved. In other words, it is the human eyethat averages out these dots and creates a grayscale. Effective digitalhalftoning or dithering can substantially improve the quality ofrendering images.

There are many known methods for halftoning, one of which is known asscreening. The simplest form of screen is a single threshold value suchas 128, and in applying this threshold to the original image acomparison is made with each pixel such that anything above 128 is setto 1 and anything below is set to zero. (Though purely a matter ofconvention, for the purposes of this description, a “1” represents aprinting or existence of a dot in the binary halftone, and “0” representan empty or omitted dot). However, basic single-level thresholding isprone to graininess and other deficiencies and generally does not createa very pleasing image in comparison to other methods.

Since basic thresholding techniques were first developed, many improvedand alternate methods have been designed. One method transforms a grayscale image to a halftone image by means of a dither matrix. The dithermatrix occupies a physical space and has numerous elements, each with anindividual value. The dither matrix is mapped over the image to generatethe halftone by a comparison of each pixel with the dither matrix valuewhich overlays it. For a gray scale image that is larger than the dithermatrix, the dither matrix is replicated or tiled to cover the entireimage. As a result, the halftone image created has the same number ofgray level patterns as the number of gray levels in the gray scaleimage. A darker area in the gray scale image is represented in thehalftone image by gray patterns with more dots.

In order to generate a halftone images using the above method, thedither matrix must be carefully designed: a fully random pattern wouldcreate a halftone image that is noisy, corrupting the content of theimage. Accordingly, the values associated with each pixel or address ofthe dither matrix are assigned specific thresholding values associatedwith the desired ordering and location in which pixels will be turned“on” as tone is added from one gray level to the next.

One prior art method of designing a dither matrix is known as thevoid-and-cluster method. A general discussion of this method can befound in “The Void and Cluster Method for Dither Array Generation” byRobert Ulichney, published in IS&T/SPIE Symposium on Electronic Imaging:Science and Technology, San Jose, Calif., 1993.

Another method of generating dither patterns or “screens” is found in“Perception of binary texture and the generation of halftone stochasticscreens” by J. Dalton, published in IS&T/SPIE 1995 InternationalSymposium on Electronic Imaging: Science and Technology, San Jose.Calif., 1995.

Another dither matrix approach is described in U.S. Pat. No. 5,317,418,“Halftone Images Using Special Filters” which is incorporated byreference herein. This approach, stochastic in nature, producesscattered dots resulting in very uniform patterns in the absence ofdot-to-dot interactions in the printing engine.

Also, yet another variety of filtering to produce dither patterns andrelated matrixes is described in U.S. Pat. No. 6,335,989, “HalftonePrinting Using Donut Filters”, which is also incorporated by referenceherein.

However, one shortcoming common to conventional dithering techniques isthat they are designed to operate on a pixel grid having substantiallysymmetric resolution. Certain output devices have a degree of sub-pixeladdressability that provides an additional degree of resolution,typically greater in one direction of the pixel grid than the other. Forinstance, some laser printers may have a horizontal sub-pixel resolutionof 2, 3 or more sub-pixels of resolution or addressability for everypixel. Accordingly, for known methods of halftoning developed to operateon a substantially symmetric grid design, use of sub-pixels can createproblems and/or, most notably, the benefits of higher resolutionattendant to sub-pixels are not fully recognized.

One advantage of using addressable sub-pixels in rendering halftoneimages is that it allows the addition of tone to be distributed amongmultiple other pixels or dot clusters. For example, an output devicewithout sub-pixel addressability (or having it but unable to utilize itwithout a method of generating halftones for controlling thedistribution of the sub-pixels) would be limited to applying additionaltone by adding single whole pixels at a time. Conversely, the ability toaddress sub-pixels has the advantage of allowing the addition (ordeletion) of tone from one graylevel to the next such that tone of evena single pixel dot value can be distributed among multiple other pixelsor dot clusters.

What is needed is a technique that enables the design of dither matricesfor creating half tone images that can take advantage of sub-pixeladdressability of certain output devices, even in circumstances wherethe sub-pixel resolution is asymmetric. Moreover, and particularlydesirable, is a solution allowing for the use of sub-pixel resolutionusing known or conventional dither matrix design methods that work onsymmetric grids; thus, a solution having a way of applying such knownmethods to the asymmetric grids inherent of sub-pixels.

SUMMARY OF THE INVENTION

The present invention provides a method of generating dither matricesfor converting from a gray scale image to a halftone image withsub-pixel characteristics, and doing so using known dithering matrixdesign methods. The invention involves the use of an intermediate,hypothetical, super-resolution grid. The super-resolution grid is usedas a means of extending conventional dither matrix generation methods tothe design of dither patterns for output devices having sub-pixeladdressability.

In the case of a sub-pixel resolution of S sub-pixels per pixelextending in one direction, the size of a super-resolution grid to becreated is directly determined from the original grid multiplied by thefactor S in both directions. The dither outputs are generated for graylevels on the super-resolution grid using conventional methods, whichare then converted to sub-pixel grid by averaging down thesuper-resolution grid by factor S along the direction of the patternthat does not have sub-pixel resolution. Dither outputs or filteroutputs are processed versions of a dither pattern corresponding to aparticular gray level. Such outputs are used in determining incrementaltone modulation, i.e. the selection of where to add or delete tone tocreate the desired grayscale. Thus, according to one embodiment of thepresent invention ultimate selection of which sub-pixel(s) to modulateis made on the sub-pixel grid pattern using the dither output convertedfrom the super-resolution grid. The resulting sub-pixel grid isasymmetric in size, corresponding (1) directly to the original griddimension in the direction without sub-pixel addressability, and (2) bya factor S larger than the original grid in the direction in whichsub-pixel resolution exists. Accordingly, when a half-tone image isprinted, it will appear dimensionally correct in relation to theoriginal grid, because the sub-pixels are narrower by the same factor S.

Accordingly, in one embodiment of the invention, a sub-pixel grid andsuper-resolution grid are created for an original pixel grid, and thedither outputs are generated based on the super-resolution grid.Subsequently, such output of the super-resolution grid is converted tothe sub-pixel grid by averaging down from the super-resolution grid sizeto achieve the corresponding sub-pixel grid size.

In another embodiment of the invention a dither matrix is created fromthe combination of a first subset of dither patterns, corresponding tocertain light tone gray levels, created using conventional ditheringmethods applied to the regular pixel grid, and a remaining subset ofdither patterns generated using a super-resolution grid. The firstsubset of dither patterns generated on the regular pixel grid are thanscaled up to the size of a sub-pixel grid by replication of cells in thedirection of the sub-pixel resolution by a factor S, which is theresolution of sub-pixels per pixel. The second, remaining subset ofdither patterns are generated using the super-resolution grid toiteratively create dither outputs which are converted to the sub-pixelgrid by averaging down the size of the super-resolution grid by factor Sin the direction not having sub-pixel resolution/addressability,whereupon such converted outputs are used to find the best location foradding (deleting) for each additional sub-pixel modulation of tone.Through the iterative generation of dither outputs on thesuper-resolution grid and addition/deletion of tone on convertedsub-pixel outputs, the desired set of dither patterns are obtained foreach desired gray level and of the appropriate sub-pixel resolution. Thetwo subsets of dither patterns, now of a common dimensional scale, thatof the sub-pixel grid, are combined to create a complete dither matrixfor N level grayscale.

Accordingly, an object of the present invention is to create a gridsystem that can be used to modulate the addition or deletion ofsub-pixels by any known or conventional dither matrix design method thatuses symmetric pixel grids. By known or conventional dithering methodswhat is meant is any number of dithering techniques that operate on asymmetric grid in generating an output dither matrix, such that use ofthe present invention will allow for such method to be used inasymmetric sub-pixel addressability applications.

DESCRIPTION OF THE DRAWINGS

The present invention is described with respect to particular exemplaryembodiments thereof and reference is made to the drawings in which:

FIG. 1A shows an example of the relation of sub-pixel resolution on ageneric pixel grid. shows a schematic of a super-resolution gridaccording to the present invention;

FIG. 1B shows an example of the different effect in applying tone usingsub-pixels versus conventional whole pixel tone modulation;

FIG. 2 shows the relationship between a representative pixel-grid [p,q]and corresponding sub-pixel grid [m,n] and super-resolution grid [i,j];

FIG. 3 is a flow diagram for generating a dither matrix according to thepresent invention;

FIG. 4 is a flow diagram another variation of generating a dither matrixaccording to the present invention;

FIG. 5 is a flow diagram of a preferred embodiment of the presentinvention using a donut filter;

FIG. 6A shows a halftone image on a super-resolution grid generatedaccording to the present invention using a donut filter; and

FIG. 6B shows a halftone image on a sub-pixel grid correlating to thesuper-resolution grid of FIG. 6A, generated according to the presentinvention using a donut filter.

DETAILED DESCRIPTION OF THE INVENTION

A method of generating a halftone image for an output device, mostnotably printer devices, having sub-pixel addressability is disclosed. Adigital output device, for example and without limitation, a laserprinter, can for each individual addressable pixel either print a dot ornot print a dot: it is a binary 1 or 0 process. And each pixel is justone location on an addressable grid. Some devices, however, have agreater level or degree of resolution in one direction (e.g.,horizontal) than in the other direction (e.g., vertical) resulting fromaddressability at the sub-pixel level.

In FIG. 1A a pixel grid 102 has a plurality of pixels across itssurface, and each individual pixel 104 has a greater resolution oraddressability in the horizontal direction, such that each pixel 104 iscomprised of sub-pixels 106 a and 106 b. Thus, any particular device mayhave a level of sub-pixel addressability whereby each pixel is comprisedof S sub-pixels that represent a factor of resolution in the directionof the sub-pixel addressability. For grid 102; each pixel 104 has twosub-pixels, thus a sub-pixel factor S=2. However, it should be notedthat other orders of resolution or sub-pixel factors may be employed, asfor example, alternative pixel grids 105 and 107 show grids withsub-pixel factors, S, of 3 and 4, respectively.

FIG. 1B shows pixel grid 108 which represents a current graylevel withcertain of its pixels printed black, indicated, for example, as pixel110 (and other analogous pixels in grid 108). When implementinghalftoning techniques, an advantage of sub-pixel addressability is thatit allows improved tone modulation, the addition (or deletion) of toneto thresholding screens from one graylevel to the next such that tonemodifications can be distributed among multiple other pixels or dotclusters. In generating screens for additional grayscales, it iscommonly the case that the next grayscale is made from the addition ofone or more pixels to the then current grayscale pattern. Thus, withconventional application of known methods, pixel grid 108 can addadditional pixel 112 to create an incremental grayscale screen 116.However, this has some disadvantages associate with the choice of whereto add pixel 112. It can be seen there is no place on grid 108 thatpixel 112 can be added in creating grid 116 in which it does not touchanother pixel, which may result in potentially undesirable clustering orpatterning. For instance, even if pixel 112 is placed at location 120(and we assume that pixel grid 108 and its dotted pattern is continuousor tiled edge-to-edge) then there is another pixel-dot 122 with whichadded pixel-dot 120 is contiguous. And, in the case of printing engineswhere dot-to-dot interactions are present, such as in laser printers, byway of example, such interaction can produce patterns that are rough andgrainy.

Conversely, using sub-pixels, the same tone can be added but distributedamong several other pixel-dots. So, for comparison, in FIG. 1B, thereare shown at 114 three sub-pixels equal to one pixel (i.e., S=3); thus,the sub-pixels shown at 114 represent the same tone of single pixel dot112. However, in adding the equivalent tone of a single pixel-dot toscreen 108 to create 118, sub-pixels 114 can be distributed among thethree different points indicated at 124. Thus, with sub-pixels, the sameadditional tone of a single pixel can be added in a distributed fashionamong several dot clusters (in this case among three different pixelclusters), creating a smoother attenuation of tone from one gray scaleto the next.

In addition to distributing the same tone of a single pixel, usingsub-pixels it is also possible to employ a finer level or granularity insimulating a grayscale by adding less than a whole pixel: it is notrequired that multiples of sub-pixels equaling whole pixels be used asjust described. Rather, single sub-pixels can be incrementally added indeveloping screens appropriate to a particular grayscale. Thus, tone canbe attenuated at the sub-pixel level by modulating the addition (ordeletion) of tone a single sub-pixel at a time. FIG. 1B finally showsscreen 126 which has been incremented from screen 118 by adding a singlesub-pixel 128. In either case (adding multiples of whole pixels orsingle sub-pixels), as a result, any error is more diffused resulting ina smoother halftoning result.

It should be noted for clarity that pixel dot 122 and sub-pixel dot 128are shown in a lighter shade for highlighting there locations to thereader, and it should be appreciated that in the present description thepixels and sub-pixels referred to are binary outputs (either a dot or nodot), and the use of shaded elements is for illustrative purposes only.

FIG. 2 shows pixel grid 200 characterizing an original pixel griddimensionally. In this example, the output device or ultimate renderingmethod has a sub-pixel resolution and addressability in the horizontaldirection of two sub-pixels per pixel, or S=2, as indicated at 216.Accordingly, the pixel grid 200 needs converting to an appropriatesub-pixel grid 202 and super-resolution grid 204 to resolve thesub-pixel factor. The use of a sub-pixel factor S=2, as persists throughthe example of FIG. 2, is by way of example only, and alternativeembodiments and implementations of the present invention may use anyvariety of sub-pixel factors as is indicated by the circumstances of thethen-immediate application.

Pixel grid 200, defining a physical space [p,q], is converted to acorresponding sub-pixel grid 202. Specifically, and with reference tothe example of FIG. 2, with S=2, sample pixel 208 is replicatedhorizontally to create sample sub-pixels 208 a and 208 b, and this isdone for all pixels of pixel grid 200. In converting, pixel grid 200 tosub-pixel grid 202, the space [p,q] is mapped to a new space [m,n] byreplicating the pixel grid according to the sub-pixel factor S.Replication is essentially the multiplication of the grid in a directionwhereby the value held by each individual pixel is duplicated or“replicated” a number times, creating a set of S replicated cells alongthe direction of replication in the newly formed grid for each formerindividual pixel.

Importantly, the replicated pixel addresses, or cells, and their valuesare extended in the replication process longitudinally along thedirection of replication, such that each subset of replicated cellscorresponding to a specific replicated pixel are contiguous. Forexample, in FIG. 2, in the horizontal replication step from pixel grid200 to sub-pixel grid 202, each pixel is replicated by a multiple of 2.Specifically, sample pixel 208 is filled, representing a value of “1”,and replication results in two cells, 208 a and 208 b, in sub-pixel grid202 having the same value (i.e., they are filled). Moreover, thereplication process extends these two cells along the direction ofreplication (in this example horizontally) and the two cells arecontiguous. This process is the same for all pixels of grid 200 whenreplicated to generated sub-pixel grid 202, regardless of the value ofthe particular pixel or cell; it is only for the point of example inthis description of the replication step that attention is pointedspecifically at pixel 208 and corresponding cells 208 a and 208 b.

The replication step 210 just described is directly analogous, then, increating the super-resolution grid 204, by replication step 212. Inreferring again to FIG. 2, with attention drawn to example pixel 208,when replicating in the vertical direction from sub-pixel grid 202 tosuper-resolution grid 204, the value of original pixel 208 is againduplicated and extended in the direction of replication, this timevertically, as cells 208 c and 208 d. Again, the replicated cells arecontiguous. It is important to note that, although FIG. 2 demonstratesthe replication of pixel grid 200 in a first direction to createsub-pixel grid 202 and then replication of sub-pixel grid 202 in asecond direction to create super-resolution grid 204, one can generatethe super-resolution grid 204 directly from pixel grid 200 byreplicating and extending grid cells in both direction simultaneously.It is purely by way of example and without limitation that FIG. 2depicts the relation between grid 200, sub-pixel grid 202 andsuper-resolution grid 204, and the various relations of the three gridforms will be evident to one skilled the art.

Another step depicted in FIG. 2 is that of averaging down in order totranscribe from super-resolution grid 204 to obtain a sub-pixel grid202. In the example shown, this is indicated as vertical averaging 214in which the resolution of the super-resolution grid 204 is reduced inthe vertical direction, resulting in the appropriate resolution ofsub-pixel grid 202. Averaging down, or vertical averaging as shown at214, is the step of condensing the values held in multiple adjacentcells (along the direction being condensed or averaged down) to areduced number of cells or single sub-pixel. It should be reminded thatthe reference to “vertical” averaging in FIG. 2 is only by example andthe concept of “averaging down” can be made in any appropriate directionto reduce the resolution of a super-resolution grid to that of thesub-pixel grid. Thus, “down” refers to reducing the number ofaddressable spaces or cells, and “averaging” indicates any number ofknown methods of obtaining a single value from several values, forexample, reducing from the two adjacent and aligned (along the directionof reduction/averaging) cells 208 a and 208 c of grid 204 to the singlecell 208 a of grid 202. Averaging may be a simple calculation of meanvalue (sum of the values divided by the number of values), it may be aweighted averaging, or it may be any number of more involved methodsthat takes into consideration various factors. One such factor might be,by way of example and without limitation, specific techniques used toaccount for repeated rounding errors commonly associated with averagingeven numbers of binary values.

Sub pixel grid 202 demonstrates visually the asymmetry of theaddressable grid [m,n] as it relates to the physical space [p,q]. Thisasymmetry inhibits use of conventional screening techniques that areunable, using heretofore known methods, to make use of sub-pixeladdressability. However, as shown in FIG. 2, the asymmetry is managed bycreating a super-resolution grid 204 representing space [i,j], whichcorresponds to the sub-pixel grid 202 and also, necessarily, to pixelgrid 200. And by the methods of replication and averaging down justdescribed, it is possible to convert between grid 200, 202, and 204. Itis essential, then, that the super-resolution grid ultimately created bean isometric grid space [i,j] which is substantially dimensionallyequivalent in both directions to the real space [p,q] times thesub-pixel factor S. Thus the super-resolution grid represents equaldistances in the grid, which allows for the use of conventional screengeneration techniques, and subsequently conversion back to sub-pixelgrid [m,n] dimensions for ultimate modulation and application of tone atthe sub-pixel level.

One method of forming dither matrixes using super-resolution grids isshown in FIG. 3. In this approach, a start state 302 begins with agrayscale image with dimensions a pixel grid [p,q] and a binary outputdevice for which dither matrices are to be formed, the output devicehaving a sub-pixel addressability of S sub-pixels per pixel in a firstdirection, which sub-pixel addressability does not extend in theorthogonal second direction. At step 304, a super-resolution grid [i,j]is generated corresponding to pixel grid [p,q] by extending throughreplication pixel [p,q] in the first direction of sub-pixeladdressability, as well as in the second, orthogonal direction nothaving sub-pixel addressability.

In step 306, initial dithering outputs O_(G)[i,j] are generated fordesired gray levels G=g/g_(max) on super-resolution grid [i,j] using anyof many known dither design methods. A dither output or filter output isa processed version of a dither pattern corresponding to a particulargray level. Thus output O_(G) [i,j] is essentially a processed versiondither pattern for a gray level on the super-resolution grid, howeversuch output must be converted to a sub-pixel scale in order that choicescan be made at the sub-pixel level as to which specific location(s) areto be modulated in adding (deleting) tone. Accordingly, outputO_(G)[i,j] is converted at step 308 to an effective response E_(G)[m,n]on the sub-pixel grid by averaging down the dither output in the seconddirection. Having E_(G)[m,n] now at a sub-pixel level, selection is thenmade at 310 as to the specific location of tone modulation made (by theaddition (deletion) of tone) to specific sub-pixel(s). If at check 312the desired pixel concentration is not yet reached for the subject graylevel G=g/g_(max), then the process returns via 314 to step 306 togenerate another incremental dither output, which is converted to asub-pixel response at 308, and is then used at 310 in again selectingthe location of the next incremental addition/deletion of tone. Thisprocess continues iteratively until the desired concentration is reachedfor the subject gray level G=g/g_(max), as determined at check 312.

When the desired tone is achieved for a specific gray level G (i.e., apositive true response 312), then the gray level is incremented at 316in order that dither patterns can be generated for the next desired graylevels G=g/g_(max) by way of generating outputs on the super-resolutiongrid, which are converted to a sub-pixel resolution for selection oftone modulation. This recursive process continues (incrementing from onegray level to the next) until dither patterns have been generated forall desired gray levels, as tested at 318. Thus, for each gray level,the successive addition (or deletion) of tone for a gray level isiteratively cycled through steps 306, 308 and 310 (by return path 312and 314) until the desired gray level concentration is reached,resulting in a dither pattern for the subject gray level; and, this inturn is repeated for all desired gray levels (by loop path 316 and 318),such that the final desired dither matrix D_(G)[m,n] is ultimatelyproduced. The resulting dither matrix D_(G)[m,n] is isotropic andprintable in the real dimensions it represents, even though it is anasymmetric array, because when output or printed the array elementscorresponding to sub-pixels, though more numerous by factor S, arefractional elements of pixels in real dimensions of widths 1/S.

An alternate method of using sub-pixel addressability by way ofsuper-resolution grids to generate dither matrices is shown in FIG. 4.In this example, start state 402 is analogous to step 302 of theprevious example of the invented method: principally there is an N-levelgrayscale image of pixel grid dimensions [p,q], and desired renderingresolution having addressable sub-pixels in a first direction thatresults in sub-pixel array [m,n] that is asymmetric, owing to asub-pixel factor S in the first direction that does exist in thealternate second, orthogonal direction.

However, unlike the method shown in FIG. 3, the presently describedmethod commences at step 404 by generating dither patterns D_(G)[p,q] onthe original grid [p,q] for a predetermined subset t of N of the totaldesired graylevels (i.e., g=0, 1, 2 . . . t; G=g/g_(max)) using knowndither pattern design methods. This subsetting may be based on anynumber of reasons, one of which may be the realization that isolatedsub-pixels tend to drop out or otherwise reproduce poorly, so tone isbest added to light graylevel in whole pixels only (because dotclustering is not yet predominant). Accordingly, in some applicationsthere may be a determinable and appropriate set t, or range for t, inwhich application of conventional screening methods are sufficientwithout regard to sub-pixel resolution. These initial dither screensD_(G)[p,q] for g=[0,t] are subsequently converted by replication tosub-pixel grid resolution at 406, which will later be combined at step412 with the dither screens of the remaining gray levels generated on asuper-resolution grid at steps 408 and 410, which when combined willcreate a single dither matrix D_(G)[m,n].

Steps 408 and 410 are analogous steps of the previous drawing FIG. 3.Super-resolution grid [i,j] is generated at step 408. Using thissuper-resolution grid, dither outputs O_(G)[i,j] are created, thoughonly for the remaining desired grayscales (of the set N-t) for whichdither patterns were not originally generated on the pixel grid [p,q].The dither outputs are converted to sub-pixel scale patterns byaveraging down along the direction of the grid not having sub-pixelresolution, so as to generate effective response E_(G)[m,n]. Thesesub-pixel outputs are then used to make specific choices of tonemodulation at the sub-pixel level. And as, for FIG. 3, these steps areiteratively repeated (modulating sub-pixel tone) for each gray leveluntil the desired tone concentration is reached for each subject graylevel. Since the final dither patterns resulting from step 410 are asubset of the remaining desired dither pattern not generated at step406, the two subsets of dither patterns are combined at step 412 tocreate a complete set of dither patterns for all desired gray levels.

It is important to note that there are other reasons evident to oneskilled in the art that would suggest a grouping of a subset (t) of thetotal grayscale, and the example of light tones due to isolatedsub-pixel dropout is but one example of the application of such possiblesubsetting.

One specific method of forming dither matrices uses what is know asdonut filters and FIG. 5 shows, specifically, a method implementing thepresent invention using donut filters. Donut filtering methods generallyare described in U.S. Pat. No. 6,335,989, “Halftone Printing Using DonutFilters”, which is incorporated by reference herein. Thus the followingdescription is not intended as a complete description of known donutfiltering methods, rather as an example of the application of at leastone known dither matrix design methods, that of donut filters, increating a dither matrix using the present invention.

Referring now to FIG. 5, in this approach, as with previously describedexamples, a start state 502 exists analogous to start states 302 and402. Similar to the method shown in FIG. 3, the super-resolution grid[i,j] is generated at 504, and that super-resolution grid isproportional to the input image of grid resolution [p,q] by a sub-pixeladdressability factor, S. Employing donut filtering techniques, next atstep 506 a donut filter F_(G)[i,j] is generated on the super-resolutiongrid (Setting n=0, G=g/g_(max)) for a particular graylevel G. Next atstep 508 a minority pattern D_(G)[i,j] is formed on the super-resolutiongrid, which is then filtered at step 510 using the donut filterF_(G)[i,j] generated at step 506 to produce a filter output O^((n))_(G)[i,j].

Next, at step 512, the filter output O^((n)) _(G)[i,j], which is on thesuper-resolution grid, is converted to an effective response E^((n))_(G)[m,n], which is on the sub-pixel grid [m,n]. This is achieved byaveraging down the super-resolution grid in the direction not havingsub-pixel addressability by the factor S. With the effective response,E^((n)) _(G)[m,n], it is possible next at 514 to find location [m*,n*]where the effective response is a minimum (maximum), subject to theconstraint that D^((n)) _(G)[m,n] is a majority (minority) pixel whenG<0.5 (G>=0.5). This then leads to step 516 where the appropriateminority pixel [m*,n*] is converted to a majority pixel, e.g.,D_(G)[m*n*]=1 (where 1 represents a dot).

Having progressed through to step 516 to select the location of adding(or deleting) the next sub-pixel element, a check is then made at 518whether the desired concentration of tone has been achieved to form thecurrent gray level G (G=g/g_(max)). If in the affirmative, then theprocess proceeds to increment the gray level at 522, and either stop at520 (if g>g_(max)) or return to step 506 to begin processing andfiltering the new current gray level. In the alternative, if the desiredconcentration of sub-pixels have not been achieved after step 516 forthe then-current gray-level, as checked at step 518, then the processreturns to step 506 to again generate and filter the minority pattern(steps 506 through 510) to find the next location to add a sub-pixel dot(514 and 516). This cycle of attenuating the addition of tone bysub-pixel continues until the current graylevel G is achieved (as testedat 518). And, ultimately, by systematically incrementing g throughg_(max) (i.e., step 522) until the desired tone is achieved for eachdesired graylevel G.

It will be appreciated by one skilled in the art the foregoing describedmethod has many variations. For example, the methods described in FIGS.3 and 4 are generally iterative in nature (not unlike that describedwith respect to FIG. 5) and depend in some part on the dither designtechnique being used, such that a repeated cycling is utilized toallocate or modulate tone by sub-pixels until the desired concentrationis reached for a particular grayscale. One variation would be to combinethe concept from FIG. 4 (that of generating only a subset of ditherpatterns using super-resolution grids, the remainder produced by anothermethod) with the example of donut filtering techniques shown in FIG. 5,or alternative filtering techniques generally. Another variation mightbe, as a specific application or circumstances may call for, to use twoor more subsets of gray levels (rather than just the one subset tdescribed in relation to FIG. 4) which subsets are not contiguous. Theseand other modifications and variations may be employed without departingfrom the inventive elements herein described, as one skilled in the artwill appreciate in practicing the disclosed invention. Thus, theforegoing detailed description of the present invention is provided forthe purpose of illustration and is not intended to be exhaustive or tolimit the invention to the precise embodiments disclosed. Accordingly,the scope of the present invention is defined by the appended claims.

1. A method of generating an N gray level dither matrix for an outputdevice having sub-pixel addressability, the method comprising the stepsof: a. creating a super-resolution grid [i,j] corresponding to a pixelgrid [p,q]; b. generating the dither matrix for a sub-pixel grid [m,n]using the super-resolution grid [i,j] by (1) generating a dither outputon the super-resolution grid [i,j]; (2) converting the dither output[i,j] to an effective response on the sub-pixel grid [m,n]; and (3)using the effective response to modulate the addition or deletion oftone of at least one sub-pixel, wherein said dither matrix is comprisedof a plurality of dither patterns, each corresponding to one of the Ngray levels.
 2. The method of claim 1 wherein the step of generating thedither matrix uses a donut filtering method.
 3. The method of claim 1wherein, for each of the N gray level, steps (1), (2) and (3) arerepeated, iteratively, until the such gray level is reached as a resultof the modulation of tone of one or more sub-pixels.
 4. The method ofclaim 3 wherein the output device having sub-pixel addressability has asub-pixel resolution factor S in a first direction [p] that does notextend in an orthogonal second direction [q] whereby step (a) comprisesreplicating each pixel of grid [p,q] by the factor S in the firstdirection and the second direction to create the super-resolution grid[i,j].
 5. The method of claim 3 wherein the super-resolution grid [i,j]is substantially isotropic in relation to pixel grid [p,q] by a factorS.
 6. The method of claim 5 wherein the step of generating the dithermatrix uses a donut filtering method.
 7. The method of claim 1 whereinstep (2) further comprises averaging down in the [j] direction thedither outputs generated on super-resolution grid [i,j] to create thecorresponding effective response on sub-pixel grid [m,n].
 8. The methodof claim 1 wherein the step of generating the dither matrix usesfrequency modulation techniques.
 9. A method of generating from a sourceN-level grayscale image a dither matrix for an output device, saidoutput device having sub-pixel addressability of a factor S sub-pixelsper pixel in a first direction [p], which sub-pixel addressability doesnot extend in a second orthogonal direction [q], the method comprisingthe steps of: a. generating dither patterns for a subset t of N graylevels on a pixel grid [p,q]; b. converting the dither patterns generatein step (a) to a sub-pixel grid [m,n] by replication S times in thefirst direction [p]; c. creating a super-resolution grid [i,j] byreplicating pixel grid [p,q] by sub-pixel factor S in both the first andsecond directions; d. generating dither patterns of the remaining subsetof (N-t) gray levels using the super-resolution grid [i,j], saidgenerating step comprising, for each of the (N-t) gray levels,iteratively and until the gray level is reached as a result of themodulation of the tone values of one or more sub-pixels: i. (1)generating a dither output on the super-resolution grid [i,j], ii. (2)converting the dither output [i,j] to an effective response on thesub-pixel grid [p,q], and iii. (3) using the effective response tomodulate the addition or deletion of tone of at least one sub-pixel; ande. combining the dither patterns of steps (b) and (d) to create thedither matrix on sub-pixel grid [m,n].
 10. The method of claim 9 whereinstep (d)(ii) of converting dither outputs to corresponding effectiveresponses further comprises the step of averaging down in the [j]direction the dither outputs generated on super-resolution grid [i,j] tocreate the corresponding effective response on sub-pixel grid [m,n]. 11.The method of claim 9 wherein one or more of the dither patternsgenerated in either steps (a) or (d) is made using frequency modulationtechniques.
 12. The method of claim 9 wherein one or more of the ditherpatterns generated in either steps (a) or (d) is made using donutfilters.
 13. The method of claim 9 wherein the subset t of N grayscalesfor which dither pattern are generated at step (a) on the pixel grid[p,q] substantially correlate to a set of light tone grayscalesconsisting primarily of isolated pixel dots.
 14. A method of generatinga dither matrix of resolution [m,n] for a source image having resolution[p,q], wherein the dither matrix corresponds to the source image by asub-pixel factor S in the [p] direction and is substantially identicalto the source image in the [n] direction, such that [p,q] maps to [m,n]as [m=S*p, n=q], the method comprising the steps of: a. creating asubstantially isometric super-resolution grid [i,j] by replicating thesource image in both directions S times, such that [i=S*p, j=S*q]; b.generating using the super-resolution grid a plurality of ditherpatterns corresponding to a plurality of desired gray levels, wherebysaid generating step comprises, for each desired gray level: (1)producing a dither output on the super-resolution grid [i,j], (2)averaging down the dither output [i,j] in the [j] direction by factorsub-pixel factor S to create an effective response on the sub-pixel grid[m,n] such that [m=i, n=j/S=q], (3) and using the effective response tomodulate the addition or deletion of tone of at least one sub-pixel; andc. combining the plurality of gray level dither patterns to create thedither matrix of resolution [m,n].
 15. The method of claim 14 whereinthe steps of generating each dither pattern for a corresponding graylevel is repeated iteratively until the gray level is reached for eachdither pattern.
 16. The method of claim 14 wherein the pixel grid [p,q],sub-pixel grid [m,n] and super-resolution grid [i,j] substantiallycorrespond as [i=m=S*p, j=n*S=q*S].
 17. The method of claim 14 wherebyin step b) at least one dither pattern is made using a donut filter. 18.The method of claim 14 further comprises the step of combining: aplurality dither patterns produced in accordance with steps (a) and (b),with one or more dither patterns produced on the pixel grid [p,q] usingconventional dithering methods whereby said dither patterns arereplicated in the [p] direction to create corresponding sub-pixelpatterns on the [m,n] grid.